LESSON NOTES MENU
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus II
Topic: Calculus of Infinity
Subtopic: Improper Integrals

Overview

Proper integrals are definite integrals that have real numbers as limits of integration. However, when one (or both) of the limits is infinity then it is an improper integral. In this case we must replace the infinity with a variable and look at the limit of the integral as that variable approaches infinity. The second type of improper integrals occurs when the function being integrated has a domain restriction on the interval [lower limit of integration, upper limit of integration]. In this case we must rewrite the integral as the sum of two integrals and use limits to approach the domain restriction.

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: improper integral, diverges (divergent integral), converges (convergent integral), Gabriel's Horn

Supplemental Resources (optional)

Video: Improper Integrals, Selwyn Hollis's Video Calculus

Lesson: Improper Integrals, Dale Hoffman's Contemporary Calculus